re_airquality
Robbert Kouwenhoven
2025-04-02
library(ggplot2)
library(plotly)## Warning: package 'plotly' was built under R version 4.4.3##
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## layoutlibrary(viridis)## Warning: package 'viridis' was built under R version 4.4.3## Loading required package: viridisLitelibrary(kableExtra)## Warning: package 'kableExtra' was built under R version 4.4.3library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:kableExtra':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, uniondatasets::airquality## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2
## 3 12 149 12.6 74 5 3
## 4 18 313 11.5 62 5 4
## 5 NA NA 14.3 56 5 5
## 6 28 NA 14.9 66 5 6
## 7 23 299 8.6 65 5 7
## 8 19 99 13.8 59 5 8
## 9 8 19 20.1 61 5 9
## 10 NA 194 8.6 69 5 10
## 11 7 NA 6.9 74 5 11
## 12 16 256 9.7 69 5 12
## 13 11 290 9.2 66 5 13
## 14 14 274 10.9 68 5 14
## 15 18 65 13.2 58 5 15
## 16 14 334 11.5 64 5 16
## 17 34 307 12.0 66 5 17
## 18 6 78 18.4 57 5 18
## 19 30 322 11.5 68 5 19
## 20 11 44 9.7 62 5 20
## 21 1 8 9.7 59 5 21
## 22 11 320 16.6 73 5 22
## 23 4 25 9.7 61 5 23
## 24 32 92 12.0 61 5 24
## 25 NA 66 16.6 57 5 25
## 26 NA 266 14.9 58 5 26
## 27 NA NA 8.0 57 5 27
## 28 23 13 12.0 67 5 28
## 29 45 252 14.9 81 5 29
## 30 115 223 5.7 79 5 30
## 31 37 279 7.4 76 5 31
## 32 NA 286 8.6 78 6 1
## 33 NA 287 9.7 74 6 2
## 34 NA 242 16.1 67 6 3
## 35 NA 186 9.2 84 6 4
## 36 NA 220 8.6 85 6 5
## 37 NA 264 14.3 79 6 6
## 38 29 127 9.7 82 6 7
## 39 NA 273 6.9 87 6 8
## 40 71 291 13.8 90 6 9
## 41 39 323 11.5 87 6 10
## 42 NA 259 10.9 93 6 11
## 43 NA 250 9.2 92 6 12
## 44 23 148 8.0 82 6 13
## 45 NA 332 13.8 80 6 14
## 46 NA 322 11.5 79 6 15
## 47 21 191 14.9 77 6 16
## 48 37 284 20.7 72 6 17
## 49 20 37 9.2 65 6 18
## 50 12 120 11.5 73 6 19
## 51 13 137 10.3 76 6 20
## 52 NA 150 6.3 77 6 21
## 53 NA 59 1.7 76 6 22
## 54 NA 91 4.6 76 6 23
## 55 NA 250 6.3 76 6 24
## 56 NA 135 8.0 75 6 25
## 57 NA 127 8.0 78 6 26
## 58 NA 47 10.3 73 6 27
## 59 NA 98 11.5 80 6 28
## 60 NA 31 14.9 77 6 29
## 61 NA 138 8.0 83 6 30
## 62 135 269 4.1 84 7 1
## 63 49 248 9.2 85 7 2
## 64 32 236 9.2 81 7 3
## 65 NA 101 10.9 84 7 4
## 66 64 175 4.6 83 7 5
## 67 40 314 10.9 83 7 6
## 68 77 276 5.1 88 7 7
## 69 97 267 6.3 92 7 8
## 70 97 272 5.7 92 7 9
## 71 85 175 7.4 89 7 10
## 72 NA 139 8.6 82 7 11
## 73 10 264 14.3 73 7 12
## 74 27 175 14.9 81 7 13
## 75 NA 291 14.9 91 7 14
## 76 7 48 14.3 80 7 15
## 77 48 260 6.9 81 7 16
## 78 35 274 10.3 82 7 17
## 79 61 285 6.3 84 7 18
## 80 79 187 5.1 87 7 19
## 81 63 220 11.5 85 7 20
## 82 16 7 6.9 74 7 21
## 83 NA 258 9.7 81 7 22
## 84 NA 295 11.5 82 7 23
## 85 80 294 8.6 86 7 24
## 86 108 223 8.0 85 7 25
## 87 20 81 8.6 82 7 26
## 88 52 82 12.0 86 7 27
## 89 82 213 7.4 88 7 28
## 90 50 275 7.4 86 7 29
## 91 64 253 7.4 83 7 30
## 92 59 254 9.2 81 7 31
## 93 39 83 6.9 81 8 1
## 94 9 24 13.8 81 8 2
## 95 16 77 7.4 82 8 3
## 96 78 NA 6.9 86 8 4
## 97 35 NA 7.4 85 8 5
## 98 66 NA 4.6 87 8 6
## 99 122 255 4.0 89 8 7
## 100 89 229 10.3 90 8 8
## 101 110 207 8.0 90 8 9
## 102 NA 222 8.6 92 8 10
## 103 NA 137 11.5 86 8 11
## 104 44 192 11.5 86 8 12
## 105 28 273 11.5 82 8 13
## 106 65 157 9.7 80 8 14
## 107 NA 64 11.5 79 8 15
## 108 22 71 10.3 77 8 16
## 109 59 51 6.3 79 8 17
## 110 23 115 7.4 76 8 18
## 111 31 244 10.9 78 8 19
## 112 44 190 10.3 78 8 20
## 113 21 259 15.5 77 8 21
## 114 9 36 14.3 72 8 22
## 115 NA 255 12.6 75 8 23
## 116 45 212 9.7 79 8 24
## 117 168 238 3.4 81 8 25
## 118 73 215 8.0 86 8 26
## 119 NA 153 5.7 88 8 27
## 120 76 203 9.7 97 8 28
## 121 118 225 2.3 94 8 29
## 122 84 237 6.3 96 8 30
## 123 85 188 6.3 94 8 31
## 124 96 167 6.9 91 9 1
## 125 78 197 5.1 92 9 2
## 126 73 183 2.8 93 9 3
## 127 91 189 4.6 93 9 4
## 128 47 95 7.4 87 9 5
## 129 32 92 15.5 84 9 6
## 130 20 252 10.9 80 9 7
## 131 23 220 10.3 78 9 8
## 132 21 230 10.9 75 9 9
## 133 24 259 9.7 73 9 10
## 134 44 236 14.9 81 9 11
## 135 21 259 15.5 76 9 12
## 136 28 238 6.3 77 9 13
## 137 9 24 10.9 71 9 14
## 138 13 112 11.5 71 9 15
## 139 46 237 6.9 78 9 16
## 140 18 224 13.8 67 9 17
## 141 13 27 10.3 76 9 18
## 142 24 238 10.3 68 9 19
## 143 16 201 8.0 82 9 20
## 144 13 238 12.6 64 9 21
## 145 23 14 9.2 71 9 22
## 146 36 139 10.3 81 9 23
## 147 7 49 10.3 69 9 24
## 148 14 20 16.6 63 9 25
## 149 30 193 6.9 70 9 26
## 150 NA 145 13.2 77 9 27
## 151 14 191 14.3 75 9 28
## 152 18 131 8.0 76 9 29
## 153 20 223 11.5 68 9 30?airquality## starting httpd help server ...## doneairquality is a dataset containing daily air quality measurements in New York from May to September of 1973. The dataset contains the day of the month, the month, the temperature (in degrees Fahrenheit), wind speed (miles per hour), solar radiation (Langleys) and ozone concentration (ppb). The ozone data is obtained from the New York state department of conservation and the meteorological data comes from the National Weather service.
Upon first inspection of the data - see the 3D scatter plot - I’m interested in figuring out to what extent the ozone concentration can be explained by variations in both temperature and solar radiation.
Plot 1 - 3D plot containing temperature, ozone, solar radiation and the months
plot_ly(airquality, x = ~Temp, y = ~Ozone, z = ~Solar.R,
type = "scatter3d", mode = "markers", color = ~Month,
colors = colorRamp(c('blue', 'red'))) %>%
layout(title = "3D Scatter Plot of Ozone, Temperature, and Solar Radiation",
scene = list(xaxis = list(title = 'Temperature (°F)'),
yaxis = list(title = 'Ozone (ppb)'),
zaxis = list(title = 'Solar Radiation (watt/m²)')))## Warning: Ignoring 42 observationsThis plot is purely used to inspect the data. Obviously, lower temperatures tend to respond to days earlier in the season. In general, it looks like the higher the solar radiation and the higher the temperature, the higher the ozone concentration.
# Clean the dataset
airquality <- airquality %>%
filter(!is.na(Ozone) & !is.na(Temp))
#Linear regression
# Model 1: Ozone vs Temperature
model_temp <- lm(Ozone ~ Temp, data = airquality)
# Model 2: Ozone vs Solar Radiation
model_solar <- lm(Ozone ~ Solar.R, data = airquality)
# Model 3: Ozone vs Temperature and Solar Radiation
model_combined <- lm(Ozone ~ Temp + Solar.R, data = airquality)
# Summarizing the models
summary(model_temp)##
## Call:
## lm(formula = Ozone ~ Temp, data = airquality)
##
## Residuals:
## Min 1Q Median 3Q Max
## -40.729 -17.409 -0.587 11.306 118.271
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -146.9955 18.2872 -8.038 9.37e-13 ***
## Temp 2.4287 0.2331 10.418 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.71 on 114 degrees of freedom
## Multiple R-squared: 0.4877, Adjusted R-squared: 0.4832
## F-statistic: 108.5 on 1 and 114 DF, p-value: < 2.2e-16summary(model_solar)##
## Call:
## lm(formula = Ozone ~ Solar.R, data = airquality)
##
## Residuals:
## Min 1Q Median 3Q Max
## -48.292 -21.361 -8.864 16.373 119.136
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.59873 6.74790 2.756 0.006856 **
## Solar.R 0.12717 0.03278 3.880 0.000179 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.33 on 109 degrees of freedom
## (5 observations deleted due to missingness)
## Multiple R-squared: 0.1213, Adjusted R-squared: 0.1133
## F-statistic: 15.05 on 1 and 109 DF, p-value: 0.0001793summary(model_combined)##
## Call:
## lm(formula = Ozone ~ Temp + Solar.R, data = airquality)
##
## Residuals:
## Min 1Q Median 3Q Max
## -36.610 -15.976 -2.928 12.371 115.555
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -145.70316 18.44672 -7.899 2.53e-12 ***
## Temp 2.27847 0.24600 9.262 2.22e-15 ***
## Solar.R 0.05711 0.02572 2.221 0.0285 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.5 on 108 degrees of freedom
## (5 observations deleted due to missingness)
## Multiple R-squared: 0.5103, Adjusted R-squared: 0.5012
## F-statistic: 56.28 on 2 and 108 DF, p-value: < 2.2e-16# Extracting R-squared values and AIC
rsq_temp <- summary(model_temp)$r.squared
rsq_solar <- summary(model_solar)$r.squared
rsq_combined <- summary(model_combined)$r.squared
aic_temp <- AIC(model_temp)
aic_solar <- AIC(model_solar)
aic_combined <- AIC(model_combined)
# Create a summary table
model_comparison <- data.frame(
Model = c("Ozone ~ Temp", "Ozone ~ Solar.R", "Ozone ~ Temp + Solar.R"),
R_squared = c(rsq_temp, rsq_solar, rsq_combined),
AIC = c(aic_temp, aic_solar, aic_combined)
)
# Plot 2 + 3
ggplot(airquality, aes(x = Solar.R, y = Ozone, color = Month)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE, color = "black") +
scale_color_viridis_c(option = "C", name = "Month") +
labs(title = "Solar Radiation vs. Ozone Concentration by Month (with Regression)",
x = "Solar Radiation (Langleys)", y = "Ozone (ppb)") +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'## Warning: Removed 5 rows containing non-finite outside the scale range
## (`stat_smooth()`).## Warning: Removed 5 rows containing missing values or values outside the scale range
## (`geom_point()`).
# Add residuals and identify outliers for the temp vs ozone plot
airquality_outliers <- airquality %>%
mutate(
Residuals = resid(model_temp),
Std_Residuals = rstandard(model_temp),
Outlier = abs(Std_Residuals) > 2
)
# Plot with outliers highlighted
ggplot(airquality_outliers, aes(x = Temp, y = Ozone)) +
# Regular points
geom_point(data = subset(airquality_outliers, !Outlier), color = "blue", alpha = 0.6) +
geom_point(data = subset(airquality_outliers, Outlier), color = "red", alpha = 0.6) +
# Regression line
geom_smooth(method = "lm", se = FALSE, color = "black") +
labs(title = "Temperature vs. Ozone Concentration (with Regression and Outliers)",
x = "Temperature (°F)", y = "Ozone (ppb)") +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
These plots all show some form of correlation between the variables of interest. The solar radiation vs ozone concentration by month shows that although a high solar radiation does not necessarily mean a high ozone concentration, all high ozone concentrations do have a high(er) solar radiation. The temperature vs ozone concentration shows - apart from some high ozone outliers - a rather linear trend: the higher the temperature, the higher the ozone concentration. This makes the linear regression interesting.
# Prepare data grid for predictions
new_data <- expand.grid(
Temp = seq(min(airquality$Temp, na.rm = TRUE), max(airquality$Temp, na.rm = TRUE), length.out = 100),
Solar.R = seq(min(airquality$Solar.R, na.rm = TRUE), max(airquality$Solar.R, na.rm = TRUE), length.out = 100)
)
# Predict Ozone based on the combined model
new_data$Ozone_Pred <- predict(model_combined, newdata = new_data)
# Plotting the contour with observed data points
# Combine predicted and observed ozone values for a unified color scale
ozone_range <- range(c(new_data$Ozone_Pred, airquality$Ozone), na.rm = TRUE)
ggplot() +
# Contour of predicted ozone
geom_tile(data = new_data, aes(x = Temp, y = Solar.R, fill = Ozone_Pred)) +
geom_contour(data = new_data, aes(x = Temp, y = Solar.R, z = Ozone_Pred), color = "white") +
# Observed data points with black border
geom_point(data = airquality, aes(x = Temp, y = Solar.R, fill = Ozone),
shape = 21, color = "black", size = 3, stroke = 1, alpha = 0.8) +
# Unified color scale for both predicted and observed ozone
scale_fill_viridis_c(name = "Ozone (ppb)", limits = ozone_range, option = "C") +
# Labels and theme
labs(
title = "Observed vs. Predicted Ozone Concentration",
x = "Temperature (°F)",
y = "Solar Radiation (Langleys)"
) +
theme_minimal()## Warning: Removed 5 rows containing missing values or values outside the scale range
## (`geom_point()`).
print(model_comparison)## Model R_squared AIC
## 1 Ozone ~ Temp 0.4877072 1067.706
## 2 Ozone ~ Solar.R 0.1213419 1083.714
## 3 Ozone ~ Temp + Solar.R 0.5103167 1020.820From this plot you can see that for low ozone concentrations, the model performs not too bad. However, for higher ozone concentrations, the model severely underestimates the ozone concentration, as the dotted observations are much brighter than the modelled background color. Also, the highest observed ozone concentrations don’t show up in the most upper right corner.
kable(model_comparison, format = "html", caption = "Model Comparison Table") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)| Model | R_squared | AIC |
|---|---|---|
| Ozone ~ Temp | 0.4877072 | 1067.706 |
| Ozone ~ Solar.R | 0.1213419 | 1083.714 |
| Ozone ~ Temp + Solar.R | 0.5103167 | 1020.820 |